Inertial reference guidance systems, extensively utilized in aircraft and missile navigation applications, have traditionally employed spinning mass gyroscopes and associated electromechanical devices for performing various guidance functions, including the detection and measurement of angular rotation rates. Such devices are relatively bulky, expensive and complex, subject to drift rates difficult to control, and require an extensive number of moving parts, some of which have a corresponding short operating life.
Various apparatus utilizing more sophisticated concepts than those of the spinning mass gyroscopes to detect and measure rotation relative to a reference frame have long been known in the art of electromagnetics and, more particularly, optical physics. One of these concepts is the "Sagnac effect" manifested in the implementation of ring interferometric apparatus, and first demonstrated in now classic experiments described by Sagnac in 1913 and later by Michalson and Gale in 1925.
Ring interferometers comprise an optical or other electromagnetic wave source for generating a signal which is applied to a beam splitter or similar optical isolation device to divide the generated signal into two equivalent counter-propagating waves initially transmitted on separate paths. These paths respectively terminate at each of two ports of a closed ring configuration such that the paths are of substantially equivalent length.
The Sagnac effect can best be described and understood by characterizing the counter-propagating waves as a clockwise (CW) traveling wave and a counter-clockwise (CCW) traveling wave. If the ring configuration is rotating at a clockwise rate G.sub.I, relativistic theory explains that the counter-propagating wave travelling in the same direction as the rotation vector of the closed path (the CW wave) is observed to follow a longer optical path than the CCW wave travelling in opposition to the path rotation. The counter-propagating waves will therefore experience a differential phase shift P.sub.S (known as the "Sagnac effect" phase shift) which can be characterized in accordance with the following equation: EQU P.sub.S =[(4.pi.RL)/(L.sub.o c)]G.sub.I (Equation 1)
where R is the radius of the enclosed path, L is the actual length of the physical path, L.sub.o is the nominal wave length of the counter-propagating waves, and c is the speed of light in a vacuum.
As apparent from Equation 1, the Sagnac phase shift P.sub.s is linearly proportional to the angular rotation rate G.sub.I of the passive ring for constant wavelength optical signals. Accordingly, a system having a ring interferometer and means for detecting and measuring Sagnac phase shift is theoretically capable of use as a navigation apparatus to determine angular rotation rates. However, as described below, extensive difficulties exist in developing physically realizable interferometric apparatus suitable for implementation in aircraft and, more specifically, in developing systems capable of practically and accurately measuring Sagnac phase shifts.
The early development of practical navigational apparatus employing Sagnac interferometric principles was hindered by the bulky size of requisite instrumentation components and direct measurement difficulties due to the small magnitude of induced Sagnac phase shifts in the range of rotation rates achieved during flight. However, laser technology and the recent advances in development of low scatter mirrors and stable structural materials have rendered the Sagnac effect measurable in various prior art systems. Certain of these systems, such as those disclosed in the Podgorski U.S. Pat. No. 3,390,606, issued Jul. 2, 1968, utilize "active" medium ring configurations and are commonly known as "ring laser gyroscopes." These ring laser gyroscopes comprise tuned resonant cavities wherein the angular rotation rate of the ring configuration is proportional to an observed beat frequency between the oppositely travelling waves within the cavity. However, such active medium ring lasers have problems associated with the phenomena of "mode pulling" and "frequency lock-in" commonly known to those skilled in the art of optical system designs. These phenomena are experienced when the frequency difference between the oscillating waves becomes small, for example, less than 500 Hz. Optical coupling occurring within the active medium tends to "pull" the frequencies of the oscillatory waves together (mode pulling) and ultimately "locks" them together (frequency lock-in) into one frequency, thereby eliminating beat frequency at the low frequency differences which would be observed in ring laser gyroscopes operating in aircraft or missile navigation systems.
Rate sensing devices have also been developed utilizing "passive" ring configurations wherein the ring configuration is a tuned cavity arrangement with externally generated counter-propagating waves. As the ring configuration is rotated, the counter-propagating waves exhibit differential frequencies and, like the ring laser systems, a corresponding beat frequency is observed therebetween which is proportional to the rate of rotation. Bias variation effects such as high temperature sensitivity tend to produce inherent beat frequency instabilities when the tuned cavity ring configurations comprise adjustable mirrors or similar arrangements. If optical fibers are utilized in the ring configurations, as may be necessitated to minimize instabilities, cavity length control becomes extremely difficult.
Another problem associated with any optical system employing signals having differential frequencies is that various bias effects can operate in a non-reciprocal manner dependent upon wave frequencies. Such bias effects are cumulative over time and can result in observed finite beat frequencies even though there is no actual angular rotation of the ring configuration.
The state of the art of integrated optics and, more specifically, optical fiber and laser design is now at a stage whereby compact instrumentation comprising passive ring interferometers can be designed with coiled multiple turn fiber optic rings capable of producing a measurable Sagnac effect phase shift over a substantially wide range of rotation rates as required in aircraft and missile applications. It should be apparent from Equation 1 that increasing the number of ring turns correspondingly increases the magnitude of Sagnac phase shift for a given rotation rate. These passive ring interferometers utilize single mode counter-propagating waves and avoid the problems of active medium and dual mode systems as previously described. However, many existing rate sensing devices utilizing the aforementioned state of the art optical technology still exhibit inaccuracies caused by inherent problems such as poor resolution over wide dynamic ranges of rotation rates (e.g. low signal to noise (S/N) ratios), and sensitivity to intensity and wavelength variations of source-generated signals.
To illustrate certain of the aforementioned problems and for purposes of understanding the invention, FIG. 1 depicts, in block diagram form, a prior art rate sensor 100 having a passive ring Sagnac interferometer 101. The subsequent discussion herein regarding the Sagnac effect will be somewhat cursory in that detailed principles of such interferometers are well-known in the art and, for example, are described in Schneider, et al, Journal of Applied Optics. Vol. 17, p. 3035 et seq. (1978).
Interferometer 101 comprises a laser source 102 capable of generating an optical signal on conductor 104 having a nominal wavelength L.sub.o. Conductor 104 and other conductors described herein can comprise any one of several types of paths capable of transmitting optical signals. The optical signal on conductor 104 is applied to a beam split/recombine circuit 106 as shown in FIG. 1. The circuit 106 is an isolation/coupler circuit and divides the optical signal on conductor 104 into two equivalent counter-propagating signal waves transmitted on conductors 108 and 110. The signal waves will be referred to as the clockwise signal (CW) wave 112 as transmitted on conductor 108 and the counter-clockwise (CCW) signal wave 114 as transmitted on conductor 110. The waves 112 and 114 are applied, respectively, to the two ring ports 116 and 118 of a multiple turn fiber optic passive ring 120. Included in the path of conductor 110 is a phase bias circuit 122 which will be described in subsequent paragraphs herein. The fiber optic ring 120 is coiled such that it comprises a radius R and a path length L. The CW wave 112 and CCW wave 114 traverse the paths of ring 120 in opposite directions and emerge from the ring on conductors 110 and 108, respectively. The returning propagating waves are then applied through circuit 106 and recombined such that a combined signal wave referred to as CS wave 124 is transmitted on conductor 126 a shown in FIG. 1.
The returning CW wave 112 and CCW wave 114 will have experienced a relative Sagnac phase shift having a magnitude and directional sense linearly proportional to the angular rotation rate of the passive ring 120. If the phase shift is characterized as P.sub.s and the angular rotation of the passive ring as G.sub.I, then Equation 1 defines the proportional relationship. For purposes of subsequent discussion relating to the prior art and the principles of the invention, this proportional relationship will be referred to herein as scale factor K.sub.S, whereby P.sub.S =K.sub.S G.sub.I.
Ignoring for a moment the function of the depicted phase shift bias circuit 122 and any constant predictable phase shifts within the interferometer 101, the recombined CS wave 124 will be reflective of the Sagnac effect phase shift P.sub.s and can be applied on conductor 126 as an input signal to a photodiode 128. CS wave 124 will "impinge" on the photodiode 128 with a fringe pattern well known in the art of optical physics. The "low order" fringe pattern, that is, the areas between alternate light and dark bands near the center of the fringe pattern, will vary in intensity in accordance with the relative phase of the recombined counter-propagating waves 112 and 114 as represented by CS wave 124. The current output signal of photodiode 128 on conductor 130 is representative of the intensity of the "zero order" portion of the low order fringe pattern. For purposes of description, this intensity signal will be referred to as signal S and can be applied as shown in FIG. 1 to various readout circuits 132 which provide a measurable output signal on conductor 134 corresponding to the signal S.
As known in physical optics theory, the signal S on conductor 130 can be described in terms of the following equation: EQU S=I.sub.o cos.sup.2 (P.sub.s /2) (Equation 2)
where I.sub.o is the maximum signal intensity and P.sub.s the relativistic phase shift occurring due to the Sagnac effect as previously described with respect to Equation 1. FIG. 2 depicts the sinusoidal variation of signal S relative to the Sagnac phase shift P.sub.s. S is symmetrical about the intensity signal axis with the intensity having a value I.sub.o for a Zero valued P.sub.s. As shown in FIG. 2, if the intensity of signal S is measured as a value S.sub.1, then a corresponding magnitude of Sagnac phase shift P.sub.1 will be observed by computation in accordance with the known functional relationship between intensity signal S Sagnac phase shift P.sub.s (Equation 2). As previously described with respect to Equation 1, P.sub.s is linearly proportional to the angular rotation rate for a specific passive ring configuration and a constant wavelength signal source. Accordingly, the magnitude of signal S provides an observable determination of rotation rate G.sub.I. Other conventional circuitry can be utilized to provide indication as to the polarity, i.e. directional sense, of the phase shift and to further determine whether the phase shift is between 0.degree. and 90.degree., or 90.degree. and 180.degree., etc.
The readout circuits 132 can comprise various types of circuits for obtaining a measurement of the intensity of signal S. For example, signal S can be sampled with associated analog to digital (A/D) conversion circuitry periodically every T seconds. The resulting output of such digital mechanization can be a binary word proportionally representative of the angular rotation rate G.sub.I each period. The period T must be chosen sufficiently small to preclude loss of substantial signal information when computing the angular displacement from the samples of intensity signal S.
As previously noted, several problems exist in basic implementations of rate sensors employing passive ring Sagnac interferometers as depicted in FIG. 1 when utilized in inertial reference systems. The relationship between the intensity signal S and the Sagnac effect phase shift P.sub.s is a non-linear sinusoidal cos.sup.2 wave form as described in Equation 2. The physically realizable values of P.sub.s will be extremely small with respect to the wavelength L.sub.o. Accordingly, the actual measured intensity S.sub.1, corresponding to a Sagnac phase shift P.sub.1, will be close to the maximum "peak" of the wave form of the signal S. Therefore, measurement of changes in Sagnac phase shift by measuring changes in magnitude of signal S is extremely difficult. Thus, within this area of operation, the non-linear relationship between the intensity signal S and the Sagnac phase shift P.sub.s limits the useful range of rate measurements when utilizing conventional measurement techniques such as digital sampling. That is, any type of digital sampling to obtain an estimation of the Sagnac phase shift will be limited by the minimal sensitivity occurring at the peak of the wave form of signal S near the phase shift axis origin.
Another problem in prior art systems is related to possible intensity variations of the signal S. Such variations can readily occur due to laser source variations or transmission losses within the optical conductive paths of interferometer 101. FIG. 3 depicts the effect of signal intensity changes with the nominal wave form of signal S shown in dotted lines and the intensity varied signal shown in solid lines. As apparent therefrom, an intensity change in signal S can result in an erroneous determination P.sub.E of the Sagnac phase shift P.sub.s for a measured signal magnitude S.sub.1. This erroneous determination will thus result in an erroneous calculation of the angular rotation rate G.sub.I.
Another difficulty with interferometer 101 is the possibility of obtaining erroneous measured rates due to variations in wave length of the optical signals. For example, a typical optical beam generated through a laser diode has a wavelength which is temperature dependent and may vary in the range of 0.03% per degree Centigrade. FIG. 4 depicts the effect of wavelength changes where the intensity pattern of signal S with a nominal wave length L.sub.o is shown in dotted lines and the varied pattern of signal S with an actual wavelength L.sub.E is shown in solid lines. Again, such wavelength changes result in an erroneous determination P.sub.E of the Sagnac phase shift P.sub.s for a measured signal magnitude S.sub.1.
Another problem associated with utilizing interferometers in applications such as missile navigation systems, where substantial accuracy is required over a wide dynamic range of rotation rates, relates to the requisite resolution within the range. For example, such a navigation system can require output signals indicative of rotation rate throughout a range of 1000.degree. per second to 1.degree. per hour, i.e. a range ratio of 3.6.times.10.sup.6 to 1, assuming constant resolution within the range. If a measurement technique such as digital sampling is utilized to estimate the magnitude of signal S, a 22 bit (plus sign) binary word must be utilized for purposes of analog to digital conversion. The necessity of such large scale data words is prohibitive to the use of small scale and high speed A/D converters as required for aircraft and missile guidance control systems. Still another problem associated with the requisite wide dynamic range pertains to the signal to noise ratio. In accordance with conventional communication theory, a 131 db S/N ratio is required for a 3.6.times.10.sup.6 dynamic range. In physically realized passive rate interferometers comprising the circuitry shown in FIG. 1, the S/N ratio will actually be closer to a value of 75 db.
Certain prior art systems employing passive ring interferometers have attempted to overcome the previously-discussed problem of intensity signal insensitivity to Sagnac phase shift changes by introduction of a phase bias circuit 122 into the optical conductive path 110 as shown in FIG. 1. Circuit 122 is a conventional circuit which induces a substantially constant phase shift in wave signals transmitted on conductor 110. The externally-applied phase shift modifies the previously-described relationship of signal S to Sagnac phase shift disclosed in Equation 2 to the following: EQU S=I.sub.o cos.sup.2 1/2(P.sub.B +P.sub.s) (Equation 3)
where P.sub.B is the externally induced phase shift applied from phase bias circuit 122.
The induced phase shift P.sub.B causes the relational pattern of output signal S to be "shifted" with respect to the Sagnac phase shift P.sub.s. FIG. 5 depicts in dotted lines the relationship between signal S and Sagnac phase shift P.sub.s with no externally-induced phase shift, and further depicts in solid lines the effect on the same relationship of the induced phase shift P.sub.B. As apparent from FIG. 5, the measured intensity S.sub.1 with induced phase shift P.sub.B and corresponding to a Sagnac phase shift P.sub.1 will be on a substantially linear and "maximum slope" portion of the relational pattern. In accordance with conventional digital sampling and communication theory, such a system will be substantially more sensitive to changes in Sagnac phase shift due to angular rotation rate changes than will a system where the expected values of phase shift occur on or near peaks and valleys of the sinusoidal intensity signal wave pattern.
One known gyroscope apparatus utilizing a passive fiber ring interferometer and generally employing phase bias circuitry was invented by W. C. Goss and R. Goldstein, and is described in the "Technical Support Package on Optical Gyroscope for NASA Technical Brief", Vol. 3, No. 2, Item 25, JPL Invention Report 30-3873/NPQ-14258 published by Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., and dated October, 1978. The Goss et al optical gyroscope comprises a passive ring Sagnac interferometer for measuring rotation rates in accordance with the Sagnac phase shift principles previously discussed herein. Output signals are generated at two optical detectors having a response pattern indicative of the resultant phase shift due to angular rotation of the passive fiber ring.
A bias cell utilizing commonly-known "Faraday effect" principles is introduced into the optical paths of the interferometer to provide a constant 45.degree. advance of one wave, 45.degree. retardation of the other wave, and phase offset compensatory for the Sagnac effect phase shift. The overall effect of the bias cell is to "shift" the response pattern of the output signals such that changes in signal intensity are maximized for corresponding Sagnac phase shift changes, thereby providing maximum measurement sensitivity. A fiber optic reversing switch is also included in the optical paths to minimize the phase shift effects of such reciprocal phenomena as long-term source drift, etc. However, the Goss apparatus does not provide complete resolution to inaccuracies in measuring rotation rates with passive ring Sagnac interferometers caused by inherent problems such as sensitivity to short term source intensity variations and optical path losses, wavelength dependency, lack of sufficient signal to noise ratio and insufficient operational dynamic range.
A substantial technological advance over other rate sensing devices is described and claimed in the commonly-assigned Carrington et al U.S. Pat. No. 4,456,376 issued Jun. 26, 1984. In Carrington et al, an optical rate sensor is disclosed which substantially corresponds to the rate sensor 200 depicted in FIG. 6. The rate sensor 200 is somewhat similar to the previously-described optical rate sensor 100 in that it comprises a passive ring Sagnac interferometer 202 having a laser source 204, optical isolation/coupler circuit 206 and a multiple turn optical fiber ring 208.
The laser source circuit 204 provides a means for generating a single transverse mode linearly polarized optical signal DS on conductor 210 with a nominal wavelength of L.sub.o. Any of several types of source circuits could be utilized for the laser source circuit 204. The optical signal DS on conductor 210 is applied as an input signal wave to optical isolation/coupler circuit 206. Circuit 206 provides a means for dividing the signal DS into two substantially equivalent wave signals separately transmitted on conductors 212 and 214. These equivalent signal waves are characterized as "counter-propagating" waves for purposes made apparent subsequently herein, and are further referred to as clockwise (CW) wave signal 216 and counterclockwise (CCW) wave signal 218 transmitted on conductors 212 and 214, respectively. Waves 216 and 218 are substantially equivalent single transverse mode waves each having a nominal wavelength of L.sub.o.
The CW wave signal 216 on conductor 212 is directly applied to one ring port 220 of the optical fiber ring 208. The CCW wave signal 218 on conductor 214 is applied as an input to ring port 222 of the fiber ring 208. However, a phase modulator circuit 224 is connected intermediate the isolation coupler circuit 206 and the fiber ring 208 on the conductive path 214. The function of the phase modulator circuit 224 will be subsequently described herein.
The fiber ring 208 can be circular in structure with a radius R and a physical path length L. Ring 208 provides a preferable ring configuration necessary for operation of the Sagnac interferometer 202 and will be more functionally described in subsequent paragraphs herein. Returning to connections in circuitry associated with the isolation/coupler circuit 206, a conductor 226 is directly connected to the coupler circuit 206 and also to an input terminal of photodiode circuit 228. The photodiode 228 provides a means for generating a current signal on conductor 230 which is representative of a sampled portion of a low order fringe pattern of the wave signal appearing on conductor 226.
Connected to the photodiode 228 by means of conductor 230 is a photodiode transconductance amplifier 232 which provides a means for converting low level output current from the photodiode 228 on conductor 230 to a voltage level signal on conductor 234, with the signal level being of a magnitude suitable for subsequent sampling and analog to digital (A/D) conversion functions. Connected to an output terminal of transconductance amplifier 232 by means of conductor 234 is an anti-aliasing filter circuit 236. The filter 236 comprises a means for preventing high frequency noise signals from the voltage signal appearing on conductor 234 from folding over into the lower frequency signal associated with the time-variant angular rate after A/D sampling of the analog signal from the photodiode 228 has occurred.
The output signal of the anti-aliasing filter 236 is applied on conductor 238 as an input to a conventional sample/hold (S/H) circuit 240. Circuit 240 provides a means for obtaining sampled signals transmitted from the filter 236 on conductor 238 and is controlled by clock pulses on conductor 242 and 244 generated from master clock 246.
Connected to the output of the S/H circuit 240 by means of conductor 248 is an A/D conversion circuit 250. Circuit 250 comprises a means for converting the sampled signals transmitted from circuit 240 to digital signals for purposes of subsequent operations. The A/D circuit 250 is controlled by means of clock pulses applied on conductor 244 from master clock 246. The clock pulses operate as "start" pulses for performance of the A/D conversion. In known systems in accordance with the Carrington et al patent, the A/D circuit 250 can comprise, for example, 12 binary information bits, thereby providing a resolution of 4,096 levels per sampled signal. A conversion time of 200 nanoseconds or less is considered suitable for purposes of utilizing the rate sensor 200 in various aircraft and missile applications.
The A/D circuit 250 is directly connected by means of conductor 252 to a sample register 254 comprising a means for storage of digital information signals representative of a plurality of sampled signals from the S/H circuit 240. Register 254 can comprise, for example, a 128 "first-in first-out" (FIFO) information word memory, each word having 12 bits of information.
The A/D circuit 250 is also connected to an overflow logic circuit 256 by means of conductor 258 as shown in FIG. 6. Sample signal levels having a magnitude greater than a predetermined level would not be stored in the A/D circuit 250, and the occurrence thereof would cause a pulse to be applied to the logic circuit 256 by means of conductor 258. The logic circuit would be reset by means of clock pulses occurring on conductor 260 as generated from the master clock 246.
The logic circuit 256 would also provide two state signals to register 262. Register 262 could be equivalent in structure and design to the register 254 and provide means for storage of a plurality of clock information signals representative of clock times corresponding to the measured times of the associated signal samples stored in register 254. These representative clock signals could be applied to the register 252 by means of clock register 264 through conductor 266. Clock pulses from master clock 246 transmitted on conductors 244 and 260 could be utilized as input signals to the register 264 to provide a sequential implementation function to achieve the requisite clock signal information within register 264. Register 264 could also comprise, for example, storage for 12 binary information signals, thereby providing 4,096 clock signal levels.
The clock register 262 and the sample register 254 are connected to a central processing unit (CPU) 268 by means of conductors 270 and 272, respectively. The conductors 270 and 272 provide a means for transmitting the binary information signals stored in registers 262 and 254 directly to the CPU 268. These conductors allow bidirectional transmission and also provide a means for the CPU 268 to selectively address the information words within the registers 262 and 254. In this particular type of configuration, the CPU 268 does not provide any specific control of the operation of the various sampling, A/D conversion and register circuitry previously described herein. The circuits operate strictly under the control of the master clock 246, and CPU 268 is merely capable of addressing the registers 262 and 254 to obtain transmission of the binary information signals stored therein directly to conventional memory units within the CPU 268. Specific functions achieved by CPU 268 are more fully described in subsequent paragraphs herein.
Returning to aspects of the optical rate sensor 200 associated with the phase modulator circuit 224, the master clock 246 is directly connected to a counter 274 by means of conductor 276. Counter 274 is a conventional binary counter which provides a means for generating sequential information signals to additional circuitry subsequently described herein. The counter 274 is clocked by clock pulses provided on conductor 276 by the master clock 246. Counter 274 can, for example, comprise a 12 bit binary information storage memory sequentially incremented at a 2 MHz rate from clock pulses supplied on conductor 276. The counter 274 can also receive information signals from the CPU 268 by means of conductor 278. In addition, and as subsequently described herein, information signals provided on conductor 278 can be utilized for purposes of initialization of phase modulation cycles and selection of particular modulator patterns to be utilized.
The counter 274 is connected by means of conductor 280 to a phase state register 282 as also depicted in FIG. 6. Phase state register 282 provides a means for storage and transmission of digital information signals to which the phase modulation circuit 224 is responsive to provide a particular modulator pattern. Phase state register 282 can, for example, comprise a parallel output of 12 binary information signals with storage capability of 4,096 12-bit binary information words.
The output of the phase state register 282 is directly connected to a digital to analog (D/A) converter 284 which provides a means for converting the digital signals received on conductor 286 to corresponding analog signals which are applied as output signals on conductor 288. D/A converter 284 can be any suitable conversion circuit capable of providing latched analog output signals corresponding to 12-bit binary input signals with a conversion and settling time of less than approximately 200 nanoseconds.
The D/A converter 284 is connected by means of the conductor 288 to a phase modulator driver amplifier 290. Driver 290 provides a means for converting the analog signals transmitted from converter circuit 284 to suitable voltage signal levels on conductor 292 for operating the phase modulator circuit 224. For example, the output voltage signals on conductor 292 can comprise a 5 microseconds alternating polarity pulse pattern with amplitude variation of 0 to .+-.20 volts. A suitable loading for the driver 290 is provided by the capacitive input of the electro-optical phase modulator 224. The driver 290, converter 284, phase state register 282 and counter 274, with associated clock control from master clock 246, comprise a control means for achieving a particular pattern of phase modulation within the modulator circuit 224.
Although not shown in FIG. 6, the optical rate sensor 200 can also include a means for achieving temperature compensation for measurements of angular rotation rates. The compensation arrangement can include a temperature monitor connected to the phase modulator 224, with additional circuitry to convert monitor signals into appropriate signals capable of storage and input to the CPU 268.
In operation, the CW wave signal 216 on conductor 212 is directly applied to the ring port 220 of the fiber ring 208. Correspondingly, the CCW wave signal 218 on conductor 214 is applied through the phase modulator circuit 224 which induces a time-variant phase shift in the CCW wave 218. The magnitude of the phase modulation shift at any given time is directly dependent and proportional to the driving voltage signal applied on conductor 292 from the previously described driver 290. The CCW wave signal 218 is thus phase modulated and applied to the ring port 222 of the fiber ring 208. The wave signals 216 and 218 thus propagate in opposing directions through the fiber ring 208.
As the waves 216 and 218 propagate through and emerge from the fiber ring 208, the phase modulator circuit 224 has been driven to a different phase shift value during the transit time, since the time of duration for each level of phase shift is made to substantially correspond to the ring transit time. The counter propagating wave which appears on conductor 214 as it emerges from the fiber ring 208 is then applied to the phase modulator circuit 224 and transmitted therefrom directly to the isolation/coupler circuit 206. The counter propagating wave emerging from the fiber ring 208 on conductor 212 is directly applied to the coupler circuit 206.
Coupler circuit 206 then operates to recombine the waves 216 and 218 into a combined wave characterized as CS wave 294 transmitted on conductor 226 as depicted in FIG. 6. As previously described with respect to passive ring Sagnac interferometers in general, the counter propagating waves 216 and 218 will have a relative Sagnac phase shift therebetween which is directly proportional to the angular rotation rate G.sub.I of the passive fiber ring 208. This Sagnac induced phase shift will result in the CS wave 294 having a low order fringe pattern representative of the magnitude and direction of the Sagnac phase shift. The CS wave 294 can be characterized as the output signal wave from the passive ring interferometer 202, and having information indicative of the magnitude and direction of the Sagnac phase shift due to angular rotation rate G.sub.I of the ring 208.
The CS wave 294 on conductor 226 is then applied as an "impinging" signal to the photodiode 228. The photodiode 228 generates an output current signal on conductor 230 having an intensity representative of a given point of the "low order" fringe pattern of CS wave 294 and, accordingly, is representative of the relative phases of CW Wave 216 and CCW wave 218.
The current output signal on conductor 230 is directly applied as an input signal to the transconductance amplifier 232 which, as previously described, provides a voltage output signal on conductor 234 having a level suitable for subsequent functional operations thereon. In FIG. 6, the signal on conductor 234 is characterized as intensity signal S.
As previously described, the relationship of an intensity signal S to a Sagnac phase shift P.sub.s and fixed induced phase shift P.sub.B is shown in Equation 3. However, in accordance with the Carrington et al arrangement, wherein a time-variant nonreciprocal phase shift is applied to the counter-propagating waves 216 and 218, the relationship of the intensity signal S to Sagnac phase shift P.sub.s is the following: EQU S=I.sub.o cos.sup.2 1/2(P.sub.B (t)+P.sub.s (t)) (Equation 4)
Where P.sub.B (t) is the known induced nonreciprocal phase shift applied from phase modulator circuit 224 and P.sub.s (t) is the rate proportional Sagnac phase shift.
As described in the Carrington et al patent, the phase shift P.sub.B (t) applied through the phase modulator circuit 224 can be varied rapidly in time in a periodic manner relative to expected rates of change of rotation. This actual phase shift applied by modulator circuit 224 can be directly proportional to the driving voltage applied on conductor 292 by driver 290. An exemplary waveform for this driving voltage pattern is depicted in FIG. 7. Each level of driving voltage has a direct and proportional correspondence with a magnitude of phase shift applied by modulator circuit 224 within the range of -.pi. to +.pi. radians. The time period T.sub.p for each modulator voltage level could, for example, be a period of five microseconds or a similar duration, and would correspond to the wave transit time through the fiber ring 208. In addition, it is also possible to vary the modulator drive pattern such that T.sub.p is a much shorter time interval than the ring transit time. By utilizing such a shorter drive voltage time period, a faster rate of output of the measured angular rotation rate could be achieved.
For purposes of subsequent description, the phase modulator phase shift symbol "P.sub.B " will be understood to be a function of time t. With the phase modulator circuit 224 providing a phase shift P.sub.B proportional to the output voltage of the driver 290, and with the time-variant phase shift varied rapidly over the range of -.pi. to +.pi. radians, the pattern of the intensity signal S as a function of the modulator phase shift P.sub.B (and, accordingly, as a function of the voltage drive pattern) will appear similar to the sinusoidal functional relationship of the signal S versus Sagnac phase shift P.sub.s previously described and depicted in FIG. 2 when there is a substantially zero rate of angular rotation G.sub.I of the passive ring 208. However, the abscissa axis of this wave pattern will now be the externally applied phase shift P.sub.B, rather than the Sagnac phase shift P.sub.s as depicted in FIG. 2.
With the scanning rate of the modulator circuit 224 sufficiently rapid relative to the rate of change of angular rotation, and with a voltage drive pattern comparable to that depicted in FIG. 7, the effect of nonzero angular rotation rate of the passive ring 208 is to cause a relational pattern of signal S relative to modulator phase shift P.sub.B to translate to the left or right of the voltage drive axis origin as depicted in FIG. 8. The specific magnitude and direction of translation, characterized herein as "phase offset," can be readily shown to directly correspond to the magnitude and direction of observed Sagnac phase shift P.sub.s. Accordingly, and as shown in FIG. 8, the modulator phase shift P.sub.B corresponding to the maximum "peak" of intensity signal S which occurs at the abscissa origin when the angular rotation rate is substantially zero will correspond to the Sagnac phase shift P.sub.s. The measurement of the "peak offset" corresponding to the offset of the intensity signal from its position when zero angular rotation is applied to the fiber ring 208 will provide a determination of the Sagnac effect phase shift.
Basically, this offset is measured in units of effective modulator differential voltage where the differential time interval implied thereby is the fiber ring optical transit time. By utilizing measurement means of the peak offset as subsequently described herein to determine the Sagnac-induced phase shift, the Carrington et al arrangement overcomes a number of inherent problems previously discussed with respect to the optical rate sensor 100 depicted in FIG. 1.
For example, the rate sensor 200 includes arrangements for determining the offset of the intensity signal S relative to the modulator drive voltage by means of center biasing intensity signal S and determining zero-crossing locations immediately before and after a peak or valley. The functional relationship between the signal S and the modulator drive voltage (and to the modulator phase shift proportional to the drive voltage) after center biasing is accomplished as shown in FIG. 9, with the modulator drive voltage corresponding to the peak offset shown as voltage V.sub.s and the Sagnac induced phase shift corresponding thereto as phase shift P.sub.s. To obtain the zero-crossing locations, the S/H circuit 240 will sample the intensity signal S at various regions of the signal pattern shown as the "sampled region" in FIG. 9. In accordance with conventional communication sampling theory, the samples obtained at zero or minimum sloped regions of the intensity pattern do not substantially contribute to determination of the zero-crossing locations. Accordingly, the optical rate sensor 200 utilizes only the sample signals which correspond to the region substantially between .+-.45.degree. of the maximum sloped positions which correspond to the zero-crossing locations.
This sampled region is determined by prestorage of a magnitude level within the A/D converter 250 which corresponds to a magnitude above which the intensity signal S can be characterized as being outside of the sampled region. As the sample signals are applied from S/H circuit 240 to the A/D converter 250, they are stored in sample register 254 until a magnitude of intensity signal sample is received which is above the predetermined magnitude corresponding to the thresholds of the sampled region. When such a signal is received, a trigger pulse is applied to the overflow logic circuit 256 by means of conductor 258. Similarly, a trigger pulse is also applied on conductor 258 when the magnitude of signal samples goes from a greater value to a lesser value than the threshold levels of the sampled region.
The overflow logic circuit 256 utilizes the trigger signals applied on conductor 258 to apply start and stop signals directly to the sample register 254 and clock register 262. During the time that the intensity signal samples are within the sampled region thresholds, the A/D converter 250 sequentially applies digital signals representative of the analog sample signals to storage locations in the sample register 254. Correspondingly, the clock register 264 applies associated clock signals to the clock register 262 to provide a time correspondent of the sample signals stored in register 254.
At appropriate times as subsequently described herein, the sample signals stored in register 254 and corresponding clock signals stored in register 262 are applied to the CPU 268. CPU 268 can be any appropriate processor circuit capable of determining the zero-crossing locations of the relational signal pattern S from the samples obtained in registers 254 and 262.
Referring again to FIG. 9, the zero-crossing locations of the intensity signal pattern S are characterized as corresponding to modulator drive voltages V.sub.c1 and V.sub.c2. When these voltages have been determined, the voltage corresponding to the location of the peak offset of the relational pattern of the intensity signal S is effectively the average of voltages V.sub.c1 and V.sub.c2 and is shown in FIG. 9 as V.sub.s. As previously described, the modulator drive voltage corresponding to the intensity signal peak will directly correspond to the Sagnac induced phase shift P.sub.s which, in turn, is linearly proportional to the angular rotation rate G.sub.I.
Again referring to the inherent problems previously discussed with respect to other optical rate sensors such as sensor 100 depicted in FIG. 1, the offset position of the peak is not altered by intensity changes of signal S. Furthermore, the peak offset as determined by the average value between the voltages corresponding to the zero-crossing locations is also not altered. In addition, the determination of the peak offset by utilizing the zero-crossing locations is substantially immune to the effect of laser source wavelength changes. Accordingly, the voltage V.sub.s corresponding to the peak can be calculated by determination of zero-crossing locations regardless of the wavelength of the intensity signal corresponding thereto.
Still further, the nonlinearity of the intensity signal S relative to the phase shifts P.sub.B and P.sub.s is of no substantial concern due to the utilization of zero-crossing detection to determine the peak offset corresponding to the modulator drive voltage V.sub.s. The zero-crossing locations are utilized to infer the phase shift corresponding to the peak offset and are linear with respect to rotation rate. Additionally, by taking a substantially large number of samples of the intensity signal S over the linear portion of the cos.sup.2 waveform, certain optimal techniques to determine cross-over locations can be effected within the CPU 268 as described in subsequent paragraphs herein.
Referring to more specific detail of the phase modulation circuit 224 and associated control circuitry, the counter circuit 274 is controlled by clock pulses derived from master clock 246 and transmitted thereto on conductor 276. The counter 274 comprises a parallel 12-bit output signal which can be utilized to directly address storage locations of the register 282. Counter 274 is triggered by the clock pulses occurring on conductor 276 and provide a count output signal in the range of 0 to 4,095 levels. Counter 274 can be controlled by start and reset pulse signals from CPU 268 on conductor 278. Conductor 278 also provides a means for varying the starting count for purposes of modifying modulator scans for reasons subsequently described herein.
As the counter 274 provides sequential binary output signals applied to the phase state register 282, register 282 is responsive to these signals to address a word location therein and generate an output signal on conductor 286 corresponding to the stored information signals within the address word location. The information signals stored in these word locations correspond to digital information signals representative of particular voltage levels which will be applied to the phase modulator circuit 224 to cause phase shifts of the counter-propagating waves 216 and 218 relative to the interferometer 202 over the time of one ring transit.
The output signals from the register 282 are directly applied to the D/A converter 284 by means of conductor 286. D/A converter 284 converts the digital information signals corresponding to the modulator voltage to be applied to modulation circuit 224 to corresponding analog signals. These analog signals are transmitted on conductor 288 to the previously-described driver 290. The driver 290 provides an appropriate interface to the modulator circuit 224 and applies voltage levels on conductor 292 in accordance with the voltage drive pattern previously described and depicted in FIG. 7.
As also previously discussed, it is possible to utilize certain conventional techniques commonly known in the art of communication circuit design to enhance the determination of zero-crossing locations and, accordingly, provide relatively high resolution in determining the angular rotation rate G.sub.I of the passive ring 208. In the rate sensor 200 depicted in FIG. 6, the function can be provided in part by utilization of information processing within CPU 268. For example, the information processing and control functions can be accomplished in part by dividing the same into certain real time sequences relating to the following functions: executive sequence control, zero-crossing and peak offset determinations, optimal estimation of peak offset, output of signals representative of angular rotation rate, phase modulator scan initiation, background tasks and recovery sequences for processing of erroneous zero-crossing information signals. A sequence diagram for these functions is depicted in FIG. 10, and a timing diagram showing the relationship of circuit functions performed by circuitry external to CPU 268 to the sequential functions performed within CPU 268 is depicted in FIG. 11.
Referring to FIGS. 6 and 11, a particular phase modulation cycle can be initiated by application of a reset signal to the counter 274 from CPU 268 by means of conductor 278. The phase modulation control circuitry comprising counter 274, register 282, D/A converter 284 and driver amplifier 290 provides sequential control of the phase modulator circuit 224 such that the modulator is driven through one period of a complete phase shift modulation pattern. This particular cycle will be characterized herein, for purposes of description, as an "even" cycle. Following the occurrence of the reset signal on conductor 278 and an appropriate predetermined delay time for purposes of allowing all circuitry to reinitialize, the S/H circuit 240 and associated A/D conversion circuit 250 accumulate sample signals from the intensity signal S and apply digital information signals representative of the analog sample signals to the sample register 254, while corresponding clock information signals are applied to the clock register 262. When the digital information signals surrounding the first zero-crossing are accumulated, the signals from registers 254 and 262 are applied to the CPU 268 by means of conductors 272 and 270, respectively.
Following the transmission of signal samples around the first zero-crossing to the CPU 268, the CPU 268 operates to determine a modulator drive voltage corresponding to the first zero-crossing of intensity signal S. When the sampled magnitude of intensity signal S is again within the sampled region depicted in FIG. 9, signal samples are again transmitted to the register 254, with corresponding clock signals transmitted to register 262. When all sample signals have been received by the register 254 within the threshold magnitudes corresponding to the sampled region, the samples are again transmitted to the CPU 268. CPU 268 again operates to determine the modulator drive voltage corresponding to the second zero-crossing of intensity signal S. Following the determination of the first and second zero-crossing locations, the determination of the modulator drive voltage corresponding to the peak offset is accomplished by averaging the modulator voltages corresponding to the first and second zero-crossings as previously described. It should be noted from the timing sequence diagram in FIG. 11 that the functions of zero-crossing and peak offset determination performed within CPU 268 can occur simultaneously with sampling and A/D conversion of intensity signal S. Accordingly, the sampling and digital conversion functions of the rate sensor 200 are independent of zero-crossing and peak offset determination functions implemented by means of the CPU 268.
When the phase modulation circuit 224 has completed the "even" cycle phase shift pattern, a reset signal is again applied from CPU 268 by means of conductor 278 to the counter 274. The counter 274 is responsive to this signal to initiate a new phase modulator pattern cycle described as the "odd" phase modulator pattern cycle. During the cycle, third and fourth zero-crossing locations and modulator drive voltages corresponding thereto are determined in a manner similar to the previously described determination of the first and second zero-crossing locations. A second peak offset determination is then made which corresponds to the average values of the modulator drive voltages corresponding to the third and fourth zero-crossings.
The times of occurrence of the two peak offsets determined by utilization of the first/second and third/fourth zero-crossing locations will differ and are utilized by CPU 268 as an input to a conventional optimal estimation sequence to provide a recursive estimate of the modulator drive voltage corresponding to the peak location and, hence, the Sagnac phase shift. The CPU 268 can then determine both an incremental angle and an angular rate of rotation by means of the known parameters of the various components of rate sensor 200, and can generate signals on conductors 296 and 298, respectively, corresponding thereto.
One problem particularly associated with optical rate sensors employed in aircraft and missile applications relates to the utilization of zero-crossing locations to determine a peak offset corresponding to the Sagnac-induced phase shift. Specifically, it is preferable that two and only two zero-crossings occur within any given scan of the phase modulator circuit 224. If more than two zero-crossing locations are present, extensive circuitry would be required to determine these crossings occurring immediately before and immediately after the peak of intensity signal S corresponding to the modulator phase shift equivalent to the Sagnac effect phase shift. However, an output rate for determination of the angular rotation rate is desirable in the range of 400 Hz. Accordingly, the phase modulation circuit 294 is required to complete two phase shift scans within 2500 microseconds. For an angular rotation rate which can have a maximum of 1000.degree. per second and for an interval of 45.degree. between zero-crossings, the phase modulator circuit 224 must be capable of scanning between .+-.4.pi. radians if the central peak is to be properly tracked and detected utilizing the zero-crossing locations of the intensity signal S. However, the capability of scanning across 8.pi. radians in less than 1,250 microseconds with a 12-bit D/A conversion level for the modulator drive voltage pattern would allocate only a 0.035 microseconds maximum time per drive voltage state. Such a state time is entirely too small for utilization of the state of the art electronic components.
To overcome this problem, the nonreciprocal phase modulation scan provided by the modulator circuit 224 has an 8.pi. radians length, but is divided into multiple overlapping "scanning windows" each having a length of 2.pi. radians. By utilization of a 2.pi. scanning window length, two and only two zero-crossings are present in any given scan.
To achieve the effect of an 8.pi. scan length with scanning windows of 2.pi. radians, the CPU 268 comprises scan initialization logic capable of determining an appropriate scanning window in accordance with the relative positions of the detected peak offsets within prior modulator scans. Since the modulator scan has an effective length of 8.pi. radians, an actual 2.pi. modulator scan utilizes only 1/4 of the possible modulator voltage level states as defined by the digital information signals stored in the phase state register 282. Following a particular modulator scan, the appropriate logic circuitry within CPU 268 can determine if the current phase modulator scan window should be altered. If the central peak within the current scanning window is not substantially centered within the scan cycle, CPU 268 transmits signals on conductor 278 as depicted in FIG. 6 which cause the counter 274 to address an altered set of information storage locations within the register 282. This altered set of storage locations will then correspond to the new scanning window by applying a differing set of digital voltage signals to the D/A converter 284. Accordingly, the phase pattern produced by the phase modulation circuit 224 can be altered in an appropriate manner to ensure that only two zero-crossing locations are detected within a modulator scan. It is apparent from this discussion that scanning windows of lengths other than 2.pi. radians can also be utilized, and the scanning windows can overlap and ensure no loss of tracking of the zero-crossing locations.
Referring to the sequence diagram of FIG. 10, the controlling sequence is designated therein as "EXEC" and provides transfer of control of the CPU 268 to background tasks when zero-crossing samples are being received by external circuitry. When zero-crossing A/D sampling is completed, the EXEC sequence can be interrupted and sequential control transferred from the background tasks to the appropriate sequence. As depicted in the timing diagram of FIG. 11, the sequence providing zero-crossing determination is performed after each zero-crossing. Determination of peak location of the intensity signal is performed only after every second scan, i.e. after four zero-crossing detections. Optimal estimation of the Sagnac phase shift is also performed only after every second scan, as is the conversion of the optimally-estimated intensity signal peak offset to an angular acceleration rate signal and an incremental angle signal. Initiation of a new scan for phase modulator 224 must occur after every scan. A recovery sequence for bad zero-crossing location signals can be performed if necessary. When processing for a particular sequence has been completed, sequential control can be returned to the current background task until the next occurrence of an interrupt which will occur at the completion of the next zero-crossing A/D conversion cycle.
Exemplary embodiments of the particular sequences shown in FIG. 10 will now be described. The function of the zero-crossing detection sequence is to determine where zero-crossing locations exist in terms of equivalent differential phase modulator voltage. As previously described, the voltages corresponding to the two zero-crossing locations yield an average value corresponding to the shift of the peak with respect to its location at a zero rate of angular location. These detections can be accomplished by means of conventional methods such as "curve fitting" utilizing the principles of "linear least squares" as commonly known in the art.
The basis for deriving zero-crossing locations using linear least squares techniques is the assumption that the sinusoidal waveform of signal S (after removing its average value) near zero-crossing locations can be approximated by the following linear equation: EQU S(V.sub.z)=a+bV.sub.z (Equation 5)
where S(V.sub.z) is the magnitude of the intensity signal corresponding to a modulator drive voltage V.sub.z, a is the V.sub.z =0 value of the linear function, and b is the slope of the linear function through the zero-crossing. In accordance with Equation 5, the modulator drive voltage corresponding to the zero-crossing location is: EQU V.sub.z (S=O)=-a/b (Equation 6)
Conventional linear least squares methods can be utilized to estimate a and b and, accordingly, the modulator drive voltage corresponding to a zero-crossing location. In a physically realized reduction to practice of the invention, values of a and b for a functional relationship of signal samples of intensity signal S and corresponding time could be determined by measurements of sampled pairs of intensity signal S and time (derived from signals generated by master clock 246). For example, with the illustrative embodiment depicted in FIG. 6, a predetermined member of such signal pairs would be stored in clock register 262 and sample register 254. The gain of the transconductance amplifier 232 would be adjusted so that register words were caused to overflow for expected intensity signal samples outside of the sampled region. Accordingly, such signal samples are not included in the derivation of the zero-crossing location.
As previously described, the actual techniques for deriving the parameters of Equations 5 and 6 are commonly-known in the art. For example, such techniques are described in Advanced Engineering Mathematics, Wylie, Jr. (McGraw Hill 1966). When the zero-crossing "times" have been determined from the received signal pairs, they can be converted to corresponding differential modulator voltages. The modulator voltage corresponding to the central peak offset (and corresponding modulator phase shift) is then determined as an average of the voltages corresponding to zero-crossing locations. This peak offset voltage is independent of bias shifts in the intensity signal S; provided, of course, that such bias shifts are slow with respect to the modulator scan time.
It should be noted, however, that certain random errors can exist within determinations of the peak offset when using conventional curve fitting techniques, such as "least squares" determinations. Such errors can be caused, for example, by A/D quantization noise, laser diode intensity noise, shot noise within the photodiode 228, Johnson noise within the analog electronics and D/A uncertainty within the basic sampled voltage steps from the intensity signal S. To at least partially overcome these and other random errors, an optimal estimation sequence can be utilized within CPU 268 to better determine the peak offset voltage. Since the statistical parameters of the modulator voltage (mean, type of disturbance noise, etc.) can be readily determined, conventional sequential estimation can be utilized.
For example, a sequential Kalman filter can provide optimal estimates of the true value of the modulator drive voltage corresponding to the central peak of the intensity signal S, even with substantially noisy measurements of this peak location. Processes related to Kalman filters and apparatus thereof are well-known in the art and, for example, are described in such texts as Probability, Random Variables, and Stochastic Processes, Papoulis (McGraw-Hill 1965), and Estimation Theory with Application to Communications and Control, Sage & Melsa (McGraw-Hill, 1971).
Basically, a Kalman filter can be used to estimate, on the basis of noisy output measurements, the value of an inaccessible state variable of a system driven by stochastic input disturbances. In an optimal rate sensor in accordance with the Carrington et al invention, the Kalman filter estimation process can be used to optimally estimate the true value of the central peak modulator voltage by linearly combining past and present measurements of this modulator voltage such that the mean square errors between the true and expected values thereof are minimized. The utilization of such an optimal estimation technique is advantageous over simple averaging processes, in that it takes into account not only additive measurement noise on the central peak modulator voltage, but also the statistics of the vehicle dynamics.
Using terminology well-known in the art of statistical estimation, a state model is first derived which represents the true value of the central peak modulator voltage as a function of sensor rate correlation time, previous values of central peak voltage, and vehicle dynamics. The measured central peak voltage is represented as a function of both the true voltage value and a noise component representing residual noise from the previously-described zero-crossing/central peak determination. For each discrete Kalman filter "cycle," corresponding to a predetermined filter update rate, an "a priori" mean square estimation error is computed as a function of rate correlation time, previous mean square estimation error computations, and the statistical effects of the previously-described residual noise. The Kalman current measurement "gain" is then computed therefrom which, in turn, is utilized with previous computations to derive an optimal estimate of the central peak modulator voltage in accordance with functional processes well-known in the art.
During the Kalman filter processing, it is inherently desired to derive what is conventionally-known as the "innovations" sequence from the voltage estimates and measurements. This sequence is used for characterizing filter performance by the comparison of the square of the innovation value with the mean square estimation error which itself is derived as part of the filter computation. If the estimation mean square error is repeatedly larger than the innovations sequence value over a number of Kalman cycles, the Kalman gain may be too small to follow high rates of vehicle angle acceleration. In such instances, the filtering process parameters can be reinitialized or other appropriate strategy can be followed.
In providing a sequence for generating output signals representative of angular rotation, experience with missile guidance systems as known by those skilled in the art shows that angular rotation frequencies of a typical missile could extend up to 150 Hz. The high frequencies often result from high order "body bending" modes. In accordance with conventional Shannon sampling theory, the output data rate must be at least twice as large as the aforementioned highest frequency. If a 400 Hz update is utilized for determination of angular rate within the CPU 268, a random drift can be achieved of approximately 1.degree. per hour.
The modulator scan initiation sequence can be designed to require completion of two scans in 2500 microseconds. For example, with a .+-.1000.degree. per second maximum rate and a 22.5.degree. half angle zero-crossing interval, the phase modulator 224 must be capable of scanning .+-.4.pi. radians if the central peak is to be tracked properly using the zero-crossing circuitry previously discussed herein. Multiple overlapping scanning windows, each having a length of 2.pi. radians, can be utilized to guarantee that two and only two zero-crossings are detected in any given scan. The sequence within CPU 268 must determine the start and finish of the D/A converter 284 read-out sequence and, given the optimal estimation of angular rate, must also decide whether to stay in a current modular scan window or to decrease or increase one position.
In addition to the foregoing, it is also possible to include a "recovery" sequence within the sequential functions of the CPU 268. The purpose of the recovery sequence is to provide capability of handling "hard" measurement errors, for example, due to loss of one of the two required zero-crossings in a scan, or otherwise due to the selection cf a scan window which does not properly contain the central signal peak and its two surrounding zero-crossings. The recovery logic sequence can be readily determined by one skilled in the art of signal processing design having knowledge of systems such as the optical rate sensor 200.
In summary, the signal processing functions of the known optical rate sensor 200 comprise the sampling of the intensity signal at various times when the functional relationship between the intensity signal and the modulator phase (and modulator voltage) is substantially linear. With the use of a least squares method for data smoothing, a central peak of this functional relationship is computed. The phase shift caused by modulation which corresponds to the central intensity signal peak also corresponds to the Sagnac phase shift resulting from the angular acceleration of the fiber ring.
It should be noted that the previously described optical rate sensor 200 is substantially an "open-loop" system with respect to operation of the phase modulator 224. That is, the phase modulator voltage applied as an input to modulator 224 is substantially independent from the measured central peak offset or any other parameters determined on a real-time basis from the intensity signal S.
To some extent, however, the foregoing statement regarding open-loop operation must be modified. In the optical rate sensor 200 as disclosed in Carrington et al, optimal estimation techniques are utilized to better determine the true value of the modulator drive voltage corresponding to the central peak of intensity signal S. Given the estimate (through use of a Kalman filter) of modulator voltage and, accordingly, the angular rate G.sub.I, the particular scanning window is determined so as to better insure that two and only two zero-crossings are present in a given scan. That is, the modulator scanning window is shifted as a function of rate so as to "track" the movement of the central intensity peak as the input rate changes.
In view of the foregoing, there is some "feedback" associated with the optical rate sensor 200 with respect to phase modulator drive voltage. However, this feedback arrangement is solely directed to the function of modifying the phase modulator scanning window for purposes of maintaining only two zero-crossing locations within any given scan.
It should also be noted that information regarding the intensity signal is ignored in certain time slots, i.e. those time slots where the intensity signal is above or below certain predetermined thresholds and the functional relationship between the intensity signal and the modulator voltage is substantially non-linear. In accordance with conventional communication theory, ignoring these portions of the intensity signal results in a relative reduction of the signal to noise ratio. When the modulator voltage pattern results in a substantially sinusoidal functional relationship between the intensity signal and modulator voltage, the S/N ratio reduction will be on the order of 3 to 6 db. This reduction will necessarily result in a loss of Sagnac phase measurement accuracy.
Still further, it can be noted that the optical rate sensor 200, when used in certain applications, will be subjected to relatively low frequency applied inertial rates, e.g. 200 Hz or less. If this low inertial rate is compared with the sampling rate and the frequency of the phase modulator output, it can be seen that the intensity signal can possibly be "aliased" to D/C. That is, because there is a finite period between scanning windows, it is feasible that a low frequency angular rate could actually be erroneously measured as a constant inertial rate input.
Finally, it can also be noted that although the measurement of the inertial rate input using the foregoing processes associated with optical rate sensor 200 is substantially independent of source wavelength, the measurement is dependent on phase modulator temperature. To illustrate, the modulator phase shift P.sub.B is a function of the modulator input voltage V.sub.M in accordance with the following: EQU P.sub.B =(K.sub.d /L)V.sub.M (Equation 7)
where K.sub.d is a constant associated with the physical implementation of the modulator, and L.sub.o is the laser source wavelength. The constant K.sub.d is, however, dependent upon the temperature of the phase modulator.
Equation 1, functionally relating the Sagnac phase shift to the inertial input rate can be rewritten as follows: EQU G.sub.I =K.sub.p L.sub.o P.sub.s (Equation 8)
where K.sub.p is a physical parameter associated with the configuration of the fiber ring, e.g. ring radius, number of turns, etc. If the phase modulation P.sub.B is now set equal to the Sagnac phase shift P.sub.s, which occurs at the central peak offset of the intensity signal, then the following functional relationship exists between the modulator voltage and the inertial input rate: EQU G.sub.I =[(L.sub.o K.sub.p K.sub.d)/L.sub.o ]V.sub.M (Equation 9)
It can be noted from Equation 9 that the source wavelength terms "cancel out," with the result being independent of laser wavelength.
In addition, it can be noted from Equation 9 that the change in modulation as a function of phase modulator voltage can be calibrated by "swinging" V.sub.M sufficiently far so as to cause P.sub.B to cover a range of 2.pi.. From Equation 7, the change in phase modulation as a function of modulator voltage can be written as follows: EQU P.sub.B /V.sub.M =(K.sub.d /L.sub.o) (Equation 10)
In accordance with the foregoing, it can be seen that if deviations in source wavelength could be modeled or otherwise accurately measured, Equation 10 could be utilized to improve the accuracy of Equation 9. However, if the source wavelength cannot be accurately modeled or measured, the actual accuracy of Equation 9 is dependent upon the ability to accurately estimate or otherwise control K.sub.d over temperature. That is, the calibration provided by swinging V.sub.M sufficiently far so as to cause P.sub.B to cover a range of 2.pi. can only provide calibration of the quantity (K.sub.d /L.sub.o).
Another potential problem associated with any type of optical rate sensor adapted for use in applications such as missile control and the like, relates to the dynamic range required for sensor operation. For example, the maximum rate required of a sensor for measurement of inertial input rates may be on the order of 1000.degree./second. Correspondingly, the minimum rate measurement which may be required can be on the order of 1.degree./hour. If digital processing techniques are to be used with respect to sensor operation, such a dynamic range would require in excess of 23 bits to provide binary representation throughout the full dynamic range of operation.
Another potential problem associated with various types of optical rate sensors relates to the bias stability of commercially available D/A converters. For example, a conventional 16-bit D/A converter having the capability of representing inertial input rates up to 1000.degree./second will have a bias stability on the order of 30.degree./hour.
One problem somewhat independent of the particular optical rate sensor employed in any specific application relates to the requirement that a complete inertial reference guidance apparatus typically requires three gyroscopes. With the gyroscopes implemented by means of optical rate sensors rather than traditional components, such as spinning mass gyroscopes and associates electromechanical devices, physical size is clearly reduced. However, optical rate sensors are not inexpensive and any physical realization of an optical rate sensor requires some finite spatial area. In particular, certain of the optical and electronic elements of an optical rate sensor, such as a light source, photodetector and signal processing components, can be relatively expensive. Furthermore, certain of these and other elements may require spatial area which is of critical concern in aircraft and missile navigational systems, especially when the spatial area must be sufficient to accommodate three separate optical rate sensors.
A substantial technological advance over other rate sensing devices whereby optical and electronic components are shared among three gyroscope channels, is disclosed in the commonly assigned U.S. patent to Gubbins et al U.S. Pat. No. 4,828,389 issued May 9, 1989. A number of the concepts of optical rate sensor technology disclosed in the Gubbins et al patent are employed in the exemplary embodiment of an optical rate sensor as described in subsequent paragraphs herein, and in which an optical interface arrangement in accordance with the present invention can be employed.
Although the foregoing optical rate sensing systems, especially the Carrington et al and Gubbins et al systems, has substantially advanced the art, output signal phase errors resulting from imperfections in physically realizable circuitry can still occur. In part, these phase offset errors result from randomly varying nonreciprocal paths between two counter-propagating optical waves in the fiber ring, other than those originating because of the inertial Sagnac effect. The following discussion relates to non-reciprocal phenomenon associated with the optical paths in the interferometer portions of the optical rate sensors.
The problems earlier discussed herein can be characterized in part as "macro" level problems, i.e. measurement errors associated with wavelength variations, etc. However, when attempting to measure Sagnac effect phase offset resulting from extremely small rotation rates, other types of "micro" level errors can become important. For example, if extremely small angular rotation rates are to be measured, the phase offset error bounds associated with the circuitry itself can become limiting factors as to measurement accuracies. Any physically realizable interferometers capable of measuring angular rotation in aircraft and the like must have the capability of detecting and measuring extremely slow-varying interferometric path differences (i.e. optical path lengths differences) over physical path lengths of substantially greater magnitude.
On the other hand, the accuracy of a ring interferometer utilizing Sagnac effect principles for determining angular rotation in aircraft and the like is substantially dependent upon the "reciprocity" of physical phenomenon acting upon the propagating optical waves and resulting in perturbations. For example, in a physically realizable interferometer, it may be required to measure optical path differences (resulting from the Sagnac effect) on the order of 10.sup.-15 meters over path lengths having a magnitude on the order of 10.sup.3 meters. The resultant 10.sup.18 ratio would typically be unrealistic for measurement purposes in most types of electrical and electromechanical apparatus. The most thermally stable material exhibits expansion coefficients in the range of 10.sup.-7 per degree centigrade. Accordingly, if temperature expansion was a non-reciprocal phenomenon, temperature regulation on the order of 10.sup.-11 degrees centigrade would be required to obviate all errors resulting from temperature changes. Clearly, such regulation is unrealistic.
However, thermal expansion, like many other phenomenon acting upon the interferometer, is reciprocal in nature. That is, temperature-related effects should act on the interferometer in such a manner that the perturbations occurring on the oppositely propagating waves should cancel each other. Many other physical phenomenon acting on the ring interferometer are also reciprocal in nature, and will tend to cancel each other out with respect to the oppositely-travelling waves. In contrast, the Sagnac phase offset is clearly nonreciprocal in nature. That is, with two oppositely-propagating waves, the non-reciprocal Sagnac effect is actually doubled in the resultant recombined wave.
In accordance with the foregoing, it is desirable to minimize as many of the potential nonreciprocal effects as possible, so that the only nonreciprocal phenomenon of any significance occurring within the optical rate sensor is the Sagnac phase offset.
Other phenomena occurring within the optical rate sensor can also lead to errors in measurement of the Sagnac phase shift. For example, any physically realizable implementation of an optical rate sensor will necessarily require interconnection or other coupling of various optical wave-carrying components. Interfacing of like components does not present significant problems. However, where materials comprising coupled components differ substantially in their respective indices of refraction, significant reflections may result. For example, as described in subsequent paragraphs herein, many of the optical components of the rate sensor can be realized by use of an integrated optics chip (commonly referred to as an "IOC"). Other components are physically realized or otherwise coupled to the IOC by use of optical fibers.
The interface between these components creates an optical boundary whereby optical waves traversing the boundary will be traveling from one medium to another, and therefore are subject to conventional reflection/refraction phenomena. In accordance with conventional optical physics, and particularly in accordance with Maxwell's theory of electromagnetic fields and the well-known equations derived by Fresnel, the intensity of the reflected optical waves relative to the intensity of the impinging waves will be a function of relative indices of refraction of the IOC wave guides and the optical fibers. A more detailed analysis of optical boundary conditions is set forth in Meyer-Arendt, Introduction to Classical and Modern Optics. pp. 303-314 (Prentice-Hall 1972).
The index of refraction of conventional optical fibers (typically 1.5 for silicon-type fibers) is substantially different than the index of refraction of the IOC wave guides (typically 2.2 for lithium niobate). Accordingly, substantial reflections can occur at the optical boundaries formed between the IOC and the optical fibers. For the interface between the beam splitter and the fiber ring (assuming the beam splitter is a component of the IOC and where the optical path comprises two paths for the two counter-propagating waves), optical waves going from the IOC to the optical fiber (the "incident" waves) will be reflected back toward the beam splitter.
In accordance with the Fresnel equations, the reflected waves will be phase shifted relative to the incident waves. Further, the phase modulator intermediate the beam splitter and the interface will act to create a phase difference in the reflected waves traversing the two optical paths. These two phenomena can result in undesirable nonreciprocal effects on the phase relationship of the counter-propagating waves.
However, another primary nonreciprocal effect is of even greater importance. Specifically, when the incident wave traversing one path of the IOC waveguides toward the optical fibers impinges on the interface boundary, the reflected wave will be directed back toward the beam splitter on the same IOC waveguide path. Correspondingly, the counter-propagating incident wave traversing the second IOC waveguide path, when it impinges on the interface boundary, will cause a reflected wave to be directed back toward the beam splitter only on the second IOC waveguide path. These two reflected waves, when recombined within the recombining circuitry, will have traversed two separate and distinct paths. Although an attempt may be made to construct the two IOC wave guide paths to be as identical as possible, in length and other characteristics, any physical realization of these paths will have somewhat different characteristics. Accordingly, with the two reflection waves essentially "seeing" two different paths prior to recombination, the two waves will be subjected to nonreciprocal perturbations. The resultant effect will be a phase difference between the two reflected waves.
In fact, with the beam splitter recombining the reflected waves, the combination of the optical boundary, separate and distinct optical paths, beam splitter and phase modulator essentially create the undesirable effect of a "folded" Mach-Zender interferometer. A more detailed description of a Mach-Zender interferometer configuration is provided in Born & Wolf, Principles of Optics, pp. 312-316 (Pergamon Press 6th Ed 1980). The result of the creation of the folded Mach-Zender interferometer is an intensity signal output similar and substantially indistinguishable from the desired intensity signal output resulting from Sagnac phase shift.
The problems associated with the coupling of light into or out of an optical fiber interface can be characterized in another manner. First, it can be assumed that for the Sagnac interferometer, light is being coupled into or out of the fundamental mode of a smoothly broken or polished end face of the fiber. It can further be assumed that r represents the intensity ratio of the reflection, corresponding to the square of the corresponding Fresnel coefficients. The coefficient r can be approximated by the following equation: EQU r.apprxeq.r.sub.n =(n-1)/(n+1) (Equation 11)
where r.sub.n represents the amplitude reflection coefficient of a plane wave at a uniform dielectric interface, and n represents the refractive index at the axis of the fiber. Correspondingly, reflection of light at the end face of the fiber will result in a voltage standing wave ratio (VSWR) at the input side of the coupler in accordance with the following: EQU VRWR=(1+.vertline.r.vertline.)/(1-.vertline.r.vertline.) (Equation 12)
In accordance with the foregoing, the voltage standing wave ratio will be approximately equal to n for both input and output coupling.
As earlier noted, in a Sagnac interferometer, this reflection may considerably modify the signals representative of Sagnac phase effect. For a Sagnac interferometer employed in an inertial reference system or the like, coupling without these disturbing reflections is required, and the voltage standing wave ratio should be as close to unity as possible.
Various methods and structures have been utilized in an attempt to reduce the effects of the undesirable reflections. Several methods are discussed in Ulrich and Rashleigh, "Beam-to-Fiber Coupling With Low Standing Wave Ratio", Journal of Applied Optics, pp. 2453-2456, Vol. 19, No. 14, Jul. 15, 1980. For example, with reference to FIG. 15, it is known to apply an anti-reflective (AR) coating to the fiber end face. Dielectric AR multilayers can be fabricated with a residual power reflectivity on the order of 10.sup.-3 for a plane wave. The same reflectivity should be expected to result from such layers, when the layers are applied to the end face of a fiber. Accordingly, the coupler of FIG. 15 will result in reflection intensity coefficients on the order of 10.sup.-3. However, for interferometers applied to inertial reference systems or the like, these phase errors are still unacceptable. In addition, application of AR coatings is relatively difficult. For example, accurate thickness control of the layers on a narrow optical fiber end face is difficult, and the physical realization of low-reflectance multi-layer designs present problems in and of themselves.
Another arrangement known for attempting to reduce reflections is the use of an immersion liquid cell as simply illustrated in FIG. 16. Specifically, the end of the fiber is immersed in a liquid having a refractive index closely matching the refractive index on the axis of the fiber. Allowing for temperature variations, the remaining index difference is typically on the order of 10.sup.-2. At such an index step, the plane wave power reflection is on the order of 10.sup.-5. It is also believed that residual reflections at the immersed end face of the fiber are similarly low. However, it is also believed that an exception may exist for fibers having a thin core diameter and a large refractive index difference between core and cladding.
Further, in addition to the reflection of the end face, reflections at both surfaces of the window shown in FIG. 16 must also be taken into account. An optimum window material will have the same refractive index as the liquid at the design temperature, i.e. as the fiber core. The reflection at the window-liquid interface is then negligible. In addition, the reflection coefficient at the window-air interface will have the value r.sub.n as defined in Equation 11. If the latter interface is positioned far from the fiber end, only a small fraction of the reflected power is coupled back into the incident mode of the fiber or free space.
Although the immersion cell arrangement presents some advantages and substantial reductions in reflections, severe difficulties exist with respect to practicality of physically realized systems. For example, the method clearly results in relatively high residual reflections, and the use of a liquid would require seals at the fiber and at the window portions. In addition, an expansion volume may be necessary for operation at varying temperatures.
Ulrich and Rashleigh also describe the concept of tilting the end face of the optical fiber, as shown in FIG. 17. By tilting the end face, the reflected light flux is separated in the angular dimension from the incident mode. To further describe this concept, it can be assumed that e is the relative small angle between the normal N of the end face and the fiber axis as shown in FIG. 17. The assumption of e being relatively small permits the use of small angle approximations. For purposes of a complete understanding of the end face tilting, FIG. 18 illustrates Fermat's principle for refraction. Referring to FIG. 18, line AP can be assumed to represent a ray of light refracted at surface SS, with line PB representing the refracted light ray. Angle a represents the angle of incidence of light ray AP from the normal line NN. Correspondingly, angle b represents the angle of incidence of the refracted light ray PB relative to the normal line NN. In accordance with Snell's law of refraction, the following relationship exists between angle a and angle b: EQU sin a/sin b=n.sub.2 /n.sub.1 (Equation 13)
where n.sub.2 represents the absolute refractive index of the medium through which the refracted light ray PB is passing, while n.sub.1 represents the absolute refractive index of the medium through which the incident light ray AP is passing.
Returning to FIG. 17, in the "output" situation, and in accordance with Snell's law, the angle between N and the beam direction in free space is e'=ne, where n is the refractive index of the fiber with respect to the free space region index (i.e. 1.0). By reciprocity, for efficient input coupling, the fiber axis must be inclined by the angle (e'- e), which is approximately equal to (n-1)e with respect to the input beam. The angular separation of the reflected beam from the input direction is 2e'=2ne in this case, whereas the separation is 2e in the output case.
To determine the optimum value of e, Ulrich and Rashleigh teach that a compromise must be reached. That is, e should be as large as possible for the "best" angular separation. On the other hand, a relatively large e may reduce the coupling efficiency by introducing astigmatic aberrations of the optical wave fronts. In addition, a relatively large angle may also cause reflection loss to vary with polarization.
The concept of tilting of the end face of the optical fiber for purposes of reducing disturbing interferences is also described in Arditty et al, "ReEntrant Fiberoptic Approach to Rotation Sensing", Proceedings of SPIE, pp. 138-148, Vol. 157 (1978).
Although Ulrich and Rashleigh, and Arditty et al, generally describe the concept of tilting an optical end face of an optical fiber, several problems are still associated with these methods. In general, although antireflection coatings and angled fiber/IOC interfaces can reduce the reflected intensity to one part in ten thousand (resulting in a reduction of the interferometer bias error to a magnitude of hundreds of degrees per hour), this reduction is still insufficient to meet the requirements of most optical rate sensor or "fiber optic gyro" (FOG) applications.